The source.
y = 8a^3/(x^2+4a^2)
z=z^2+c ; the Mandlebrot set
Fractals and pre-fractals once noticed were everywhere.
They occur:
in physics in the description of the extraordinarily complex behaviour of some simple
physical systems like the forced pendulum
in the hugely complex behaviour of turbulence and phase transition.
as the foundations of what is now known as chaotic systems.
They occur in economics with the behaviour of prices and as Poincaré had suspected
in physiology in the growth of mammalian cells.
gardens. Note closely and you will see a difference between the flower heads of
broccoli and cauliflower, a difference which can be exactly characterised in fractal theory.